When I follow the instructions on this page, I get a popup message stating 'On an iPhone, iPad or iPod touch go to Settings > Apple ID. On a Mac go to System Preferences or System Settings > Apple ID'. I don't see any option on the settings for app-specific password. I tried this on MacPro M1 and iPhone 14 proMax
MacBook Pro
This "continue on" message seems to be appearing in various contexts when editing Apple Account information with a web browser. You can try editing the information as indicated in the messages by using Settings. Others have found using a different browser or simply trying again may work.
Related discussions:
every time I tried to create an app-speci… - Apple Community
"Someone in another post said to use a different browser (not Safari or whichever one you normally use). That worked for me."
"Use a computer to generate the App specific passwords. Don't use Safari or Chrome. I got it to work using Firefox on my Mac."
"the Chrome browser works for me."
Can't change Apple ID - Apple Community
"OK it just worked. No idea what was going on before. Thanks for the help anyway!"
Can't Change / Remove Apple ID Notificati… - Apple Community
Occurred while changing account information using a web browser.
Problem creating app-specific password
